His first film role was A Canterbury Tale in 1944, and he went on to enjoy a chequered film career, the high point of which was his performance as the suave murderer Louis Mazzini in the British comedy classic, Kind Hearts and Coronets (1949). He was married to the actress Joan Schofield from 1939 to 1950. They had two children.

Price struggled to lead a conventional life during a period in British history when homosexuality was still a criminal offence. On April 191954, Price tried to commit suicide by attempting to gas himself in his London home. Public sympathy led to a resurgence in his popularity and the offer of film roles. However, his private life, which included heavy gambling and an increasing reliance upon alcohol, began to affect his health, looks and career. Price's private anguish may have led to his role in the film Victim (1961), controversial at the time, which portrayed the dilemma faced by a group of gay men who were being blackmailed for their sexuality.

In 1959, he was the original "No.1" in charge of the crew of HMS Troutbridge in the first series of the long-running radio comedy series The Navy Lark but unable to continue the role in the second series owing to other work commitments, he was replaced by Stephen Murray.

In 1966, Price was declared bankrupt and moved to the tax haven island of Sark, describing it with characteristic wit as "a strategic withdrawal". This coincided with an escalation in his alcoholism. Whilst many of his contemporaries were landing major roles in both film and television, Price was constrained to appear in a series of 'B movie' horror films such as Horror Hospital, Twins of Evil and Theatre of Blood. Although some of these films have acquired a cult following, they are far from the more intellectual roles with which he was originally associated. Always an elegant actor, he ended his career on a low note. However, it is for his performance as the witty, sardonic rake Louis Mazzini that he will always be most fondly remembered. Price's portrayal of Mazzini's ruthless determination to succeed to the title of Duke Of Chalfont allowed the actor the chance to display a wider scope of acting talent than he is popularly given credit for. Although co-star Alec Guinness famously plays eight different roles, Price is also called upon to feign several different personalities, accents and characters.

Price died of heart failure resulting from a hip fracture in Guernsey at age 58 on October 61973. He is buried on the nearby island of Sark.